Question: Simplify the following expression and state the condition under which the simplification is valid: $t = \dfrac{a^2 + 5a}{a^2 - 25}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{a^2 + 5a}{a^2 - 25} = \dfrac{(a)(a + 5)}{(a - 5)(a + 5)} $ Notice that the term $(a + 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(a + 5)$ gives: $t = \dfrac{a}{a - 5}$ Since we divided by $(a + 5)$, $a \neq -5$. $t = \dfrac{a}{a - 5}; \space a \neq -5$